An extended power Lindley distribution and its application

Abstract

Abstract. This paper introduces a new ve-parameter lifetime model called the exponenti- ated Kumaraswamy power Lindley distribution, that extends the power Lindley distribution and some well-known distributions. Various structural properties of the new model including expansions for the density function, explicit expressions for the ordinary and conditional moments, residual and reversed residual life functions and mean deviations are derived. The maximum likelihood method is used to estimate the model parameters. The usefulness and exibility of the proposed model are illustrated empirically by means of two real data sets.

Resume. Ce papier introduit un modele de duree de vie a cinq variables appelee exponen- tiation du modele puissance Kumaraswamy de Lindley, qui generalise le modele puissance de la distribution de Lindley et cetaines distribitions connues. Y sont etablies dierentes proprietes structurelles di mouveau modele, y compris des developments en serie de la den- site de probabilite, une expression explicite des moments conditionnels et inconditionnels, les fonction de duree de vie (residuelles et residuelles inverses), et des proprietes relatives a la deviation par rapport a la moyenne. Les parametres ont ete estimes par la methode du maximum de vraisemblance. L'utilite et la exibility de la methode a ete montree sur deux jeux de donnees reelles.

Key words: Exponentiated Kumaraswamy-G; Maximum likelihood estimation; Moments;
Power Lindley distribution.